Simulations of quantum double models

TL;DR

This paper presents a digital simulation method for topologically ordered quantum systems based on the quantum double of finite groups, demonstrating how to prepare, braid, and fuse anyonic excitations with potential for universal quantum computation.

Contribution

It introduces a novel digital simulation approach for quantum double models, including a physical realization of the non-Abelian D(S_3) model using trapped atoms.

Findings

Simulation of topologically ordered systems with anyons

Implementation of universal quantum computation with anyons

Physical realization using optical lattices

Abstract

We demonstrate how to build a simulation of two dimensional physical theories describing topologically ordered systems whose excitations are in one to one correspondence with irreducible representations of a Hopf algebra, D(G), the quantum double of a finite group G. Our simulation uses a digital sequence of operations on a spin lattice to prepare a ground "vacuum" state and to create, braid and fuse anyonic excitations. The simulation works with or without the presence of a background Hamiltonian though only in the latter case is the system topologically protected. We describe a physical realization of a simulation of the simplest non-Abelian model, D(S_3), using trapped neutral atoms in a two dimensional optical lattice and provide a sequence of steps to perform universal quantum computation with anyons. The use of ancillary spin degrees of freedom figures prominently in our construction and provides a novel technique to prepare and probe these systems.